Prepare fries according to package directions until golden brown and crisp, about 20 minutes.
While fries cook, whisk together mayonnaise, relish, vinegar, paprika, 2 tablespoons mustard, 2 tablespoons ketchup, 1/2 teaspoon salt, 1/2 teaspoon garlic powder, and 1/2 teaspoon onion powder in a bowl; set aside.
Heat oil in a large skillet over medium-high heat. Add ground beef in large pieces; sprinkle with black pepper and remaining 1/2 teaspoon each salt, garlic powder, and onion powder. Cook, undisturbed, until deeply browned on the bottom, about 3 minutes. Turn and cook, breaking into large crumbles and stirring occasionally, until browned and cooked through, 2 to 3 more minutes. Stir in remaining 1 tablespoon each mustard and ketchup; cook, stirring gently, until coated and slightly caramelized, about 1 minute. Remove from heat.
Divide hot fries evenly among 4 shallow bowls, arranging as a base. Spoon hot beef mixture into one section of each bowl. Arrange lettuce, tomatoes, and pickles in separate sections around beef. Sprinkle evenly with Cheddar cheese and drizzle evenly with reserved sauce, to taste. Serve immediately with more sauce on the side. Recipe developed by Marianne Williams